Question

1. X Bank holds Assets and Liabilities whose average durations and dollar amounts are as shown in the following table:

Asset and Liability Items	Avg. duration in years	Dollar amount in millions
Investment Grade Bonds	10	$50
Non-deposit Borrowings	0.10	20
Consumer Loans	7	250
Commercial Loans	4	400
Deposits	1.10	600
Subordinated Notes	2.80	80
Treasury Bonds	8.25	120

   

1. Calculate the weighted-adjusted duration of X’s assets portfolio and liability portfolio.
2. What is the leverage-adjusted duration gap?
3. If the ALM team speculatively take this position, what do you think their expectations are regarding the future market rates?
4. What happens to the net worth of the bank if the interest rates increase from 6% to 7%?

Answer 1

a)Weighted-adjusted duration assets = (10*50+0.1*20+7*250+4*400)/(50+20+250+400) = 5.35 years

Weighted-adjusted duration liabilities = (1.1*600+2.80*80+8.25*120)/(600+80+120) = 2.3425 years

b) Total assets = 50+20+250+400 = 720

Total liabilities = 600+80+120 = 800

Leverage adjusted duration gap = 5.35-(800/720)*2.3425 = 2.747 years

c) Since the duration of assets > duration of liabilities & the duration gap is positive, the banks expects the interest rates to fall in near future. However, in general the banks maintain a positive duration gap to keep their cost of funding low without any expectation on future interest rates

d)

Change in value = -(size)*(duration)*(change in interest rate)

Asset side

size = $720 million; duration = 5.35; change in interest rates = 1%

Change in value = -720*5.35*1% = -$38.52 million

Liability side

size = $800 million; duration = 2.3425; change in interest rates = 1%

change in value = -800*2.3425*1% = -$18.74 million

Change in net worth = -38.52-(-18.74) = -$19.78 million

**please note that you might be confused how liability size is greater than asset size. This is because in this question only interest rate sensitive assets are included. Non interest rate sensitive assets like cash are missing